Designs, Codes and Cryptography

, Volume 38, Issue 3, pp 337–361 | Cite as

On the Algebraic Structure of Quasi-cyclic Codes IV: Repeated Roots

  • San Ling
  • Harald Niederreiter
  • Patrick Solé


A trace formula for quasi-cyclic codes over rings of characteristic not coprime with the co-index is derived. The main working tool is the Generalized Discrete Fourier Transform (GDFT), which in turn relies on the Hasse derivative of polynomials. A characterization of Type II self-dual quasi-cyclic codes of singly even co-index over finite fields of even characteristic follows. Implications for generator theory are shown. Explicit expressions for the combinatorial duocubic, duoquintic and duoseptic constructions in characteristic two over finite fields are given.


quasi-cyclic codes GDFT Hasse derivative codes over rings self-dual codes Type II codes 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Division of Mathematical Sciences, School of Physical and Mathematical SciencesNanyang Technological UniversitySingaporeRepublic of Singapore
  2. 2.Department of MathematicsNational University of SingaporeSingaporeRepublic of Singapore
  3. 3.CNRS, I3S, ESSISophia AntipolisFrance

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